Question

12. In the below figure, ABCD is a parallelogram, AE I DC and CF I AD. If AB = 16 cm, AE =
8 cm and CF = 10 cm, find AD.
D
E​

Answer 1

Given :

A parallelogram ABCD in which ,

AE perpendicular to DC,

CF perpendicular to AD,

AB = 16 cm,

AE = 8 cm,

CF = 10 cm,

To find :

Length of AD

Solution :

AB = CD ( opposite sides of parallelogram )

Area of parallelogram :-

= Base × Altitude

If Base is DC and Perpendicular is AE.

Then,

Area of parallelogram ABCD:

= DC × AE

= 8 cm × 16 cm ------------------------------------- ( 1 )

If Base is AD and CF is perpendicular ,

Then,

Area of parallelogram ABCD:

= AD × CF

= AD × 10 cm ----------------------------------------- ( 2 )

From ( 1 ) and ( 2 ) we get ,

8 cm × 16 cm = AD × 10 cm

$AD = \frac{8 \: cm \: \times 16 \: cm}{10 \: cm} \\ AD = 12.8 \: cm$

Thus length of AD = 12.8 cm.

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Answer 2

Question :-

In figure, ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

Answer :-

We have, AE ⊥ DC and AB = 16 cm

∵ AB = CD [Opposite sides of parallelogram]

∴ CD = 16 cm

Now, area of parallelogram ABCD = CD x AE

= (16 x 8) cm2 = 128 cm2 [∵ AE = 8 cm]

Since, CF ⊥ AD

∴ Area of parallelogram ABCD = AD x CF

⇒ AD x CF = 128 cm

⇒ AD x 10 cm = 128 cm2 [∵ CF= 10 cm]

⇒ AD = 128/10 cm = 12.8 cm 10

Thus, the required length of AD is 12.8 cm

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